Multi-sphere head model for dipole localization without ghost spheres

ABSTRACT

In one aspect, a computer-implemented method corrects a multi-sphere head model used in dipole localization for a set of magnetic field sensors (MEG sensors) by replacing ghost spheres with replacement spheres that are not ghost spheres. One type of ghost sphere completely encloses the brain volume but is so large that a center of the sphere is outside the brain volume. Another type of ghost sphere lies entirely outside the brain volume. Various approaches for correcting ghost spheres are disclosed.

BACKGROUND 1. Technical Field

This disclosure relates generally to generating multi-sphere headmodels, as may be used in dipole localization for magnetoencephalography(MEG).

2. Description of Related Art

In magnetoencephalography (MEG), the brain's electrical activity causesa magnetic field and this is captured by magnetic field sensors (MEGsensors) positioned at different locations around the brain. Thesesignals can be analyzed for various purposes, such as diagnosing medicalconditions, measuring brain function, and conducting research. They areespecially well-suited for detecting temporal responses. In one commonscenario, the subject undergoes different types of stimuli or performsdifferent types of activity and the resulting MEG signals are reviewedfor certain responses or characteristics. For example, if a knownstimulus is presented to the subject, the MEG signals may be observedfor a response of a certain frequency at a certain time delay after thestimulus. The presence or absence of that response may be an indicationof a medical condition. Statistical analysis can also be performedacross populations of subjects, for example between groups with andwithout a medical condition.

In many MEG applications, it is useful to have a multi-sphere model (akaoverlapping sphere model) of a person's head. A multi-sphere modelincludes one sphere for each MEG sensor. The sphere is selected to matcha local curvature of the brain surface in the area most relevant to theMEG sensor. These can then be used in the dipole localization step,which is a common step for many MEG processing pipelines. However, inmany cases, the multi-sphere model generated using conventionalapproaches results in ghost spheres. In a ghost sphere, a significantpercentage of the sphere's volume lies outside the brain. The use ofghost spheres results in models in which a large number of dipoles arelocated outside the brain, which does not match the physical reality.

Thus, there is a need for better approaches to generate overlappingsphere models, including for MEG and other encephalography applications.

SUMMARY

In one aspect, the present disclosure provides a computer-implementedmethod for correcting a multi-sphere head model used in dipolelocalization for a set of magnetic field sensors (MEG sensors) byreplacing ghost spheres with replacement spheres that are not ghostspheres. One type of ghost sphere completely encloses the brain volumebut is so large that a center of the sphere is outside the brain volume.Another type of ghost sphere lies entirely outside the brain volume.Various approaches for correcting ghost spheres are described below.

Other aspects include components, devices, systems, improvements,methods, processes, applications, computer readable mediums, and othertechnologies related to any of the above. The following examples usespheres as a basic shape, but other shapes may also be used, for exampleellipsoids.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure have other advantages and features whichwill be more apparent from the following detailed description and theappended claims, when taken in conjunction with the examples in theaccompanying drawings, in which:

FIG. 1 (prior art) is a flow diagram of a magnetoencephalography (MEG)forward model.

FIG. 2A shows a single sphere head model.

FIG. 2B shows an overlapping sphere (multi-sphere) head model.

FIGS. 3A and 3B show two types of ghost spheres.

FIG. 4 is a flow diagram for correcting ghost spheres in a multi-spherehead model.

FIG. 5 shows a family of candidate replacement spheres.

FIG. 6A shows different lines that may be used to define families ofcandidate replacement spheres.

FIG. 6B shows an area that may be used to define a family of candidatereplacement spheres.

FIGS. 7A and 7B show volumes that may be used to define a family ofcandidate replacement spheres.

FIG. 8 shows different spheres that may be used to define a maximumdiameter for a family of candidate replacement spheres.

FIG. 9 shows another family of candidate replacement spheres.

FIG. 10 shows a user interface for controlling the correction of ghostspheres.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The figures and the following description relate to preferredembodiments by way of illustration only. It should be noted that fromthe following discussion, alternative embodiments of the structures andmethods disclosed herein will be readily recognized as viablealternatives that may be employed without departing from the principlesof what is claimed.

FIG. 1 (prior art) is a flow diagram of a magnetoencephalography (MEG)forward model. In MEG, magnetic field sensors are positioned atdifferent locations around the brain. For example, the patient mayposition his head inside equipment with an array of MEG sensors or thepatient may wear headgear containing an array of MEG sensors. Thebrain's electrical activity produces a magnetic field and the magneticfield at different locations is measured by the MEG sensors. The processin FIG. 1 is a forward model, which estimates the magnetic field at eachMEG sensor for a given pattern of brain activity. This forward model canthen be used to solve the inverse problem: Given measurements of themagnetic field at each MEG sensor, estimate the electrical brainactivity that produced the measured magnetic fields.

The process has three main steps. A model of the patient's head isgenerated 110. A model of the sources of magnetic field in the brain isgenerated 120. The source model 120 is applied to the head model 110 toestimate 130 the magnetic field at each of the MEG sensors.

In this example, assume that MM slices of the patient's head areavailable. The head model 110 may be generated as follows. The MRIslices are first assembled into a three-dimensional volume model of thepatient's head, for example a three-dimensional model that representsthe patient's head as voxels 112. A surface model 114 of the relevantstructure is generated from the three-dimensional volume model. Thesurface model 114 is used to generate 116 the head model, for example asingle sphere head model (SSM) or an overlapping sphere head model(OSM). In the following examples, the head model is based on spheres butother shapes may also be used, for example ellipsoids.

FIGS. 2A and 2B illustrate the single sphere head model and theoverlapping sphere head model (also known as a multi-sphere model). Inboth figures, MEG sensors 210 are positioned around the brain 220. Inthe SSM (FIG. 2A), the patient's brain is represented by a single sphere230 based on fit to the surface model. In the OSM (FIG. 2B), thepatient's brain is represented by multiple overlapping spheres 240A-F,one for each corresponding MEG sensor 210A-F. Sphere 240A corresponds toMEG sensor 210A, sphere 240B to MEG sensor 210B, etc. The spheres 240are chosen in part to match the local curvature of the brain's surfacein the vicinity of the corresponding MEG sensor 210. For convenience,the one sphere 230 in the SSM may be referred to as a global spherebecause the same sphere is used for all MEG sensors 210, and each of thespheres 240A-F in the OSM may be referred to as local spheres. Returningto FIG. 1, the SSM/OSM 116 is used to model the propagation of magneticfields from sources within the brain to the MEG sensors.

The sources within the brain are typically modelled 120 as dipolesources. The synaptic electrical activity in the brain may be modelledas current dipoles. The model includes a distribution 122 of dipolesthroughout the volume of the brain. Given a dipole at a certain locationof the brain and given the model of the brain volume (e.g., OSM or SSM),the magnetic field created by each dipole is simulated 124. Thecontributions of all dipoles are aggregated 130 to estimate the totalmagnetic field at each MEG sensor. This is referred to as the lead fieldmatrix.

Conventional approaches to generating the OSM (step 116 above) mayresult in local spheres that are “ghost spheres.” In conventionalapproaches, each local sphere 240 is generated based on the curvature ofthe brain's surface in the local vicinity of the corresponding MEGsensor 210. However, if there is a sparsity of sample points for thebrain's surface or if the points are excessively noisy or if the brain'ssurface has an unusual local curvature, the resulting sphere may notwork well with later steps of MEG processing.

FIGS. 3A and 3B show examples of two types of ghost spheres. In eachfigure, a local surface patch 314 of the brain closest to the MEG sensor310 can be used to define outward and inward directions relative to thebrain. The outward direction is the direction from the local surfacepatch 314 towards the MEG sensor 310, and the inward direction is thedirection from the local surface patch 314 away from the MEG sensor 310.

In FIG. 3A, the sphere 340A with center 342A was generated for MEGsensor 310A. However, the surface model of the brain results in a sphere340A that is large compared to the brain. In this example, the center342A of the sphere is inwards of the local surface patch 314A. That is,the center 342A of the sphere and the MEG sensor 310A are located onopposite sides of the local surface patch 314A. Usually, this isdesirable because the volume of the brain is located on the inward sideof the local surface patch. However, the sphere has such a largediameter that the center 342A of the sphere falls outside the brainvolume. This may be problematic because fifty percent or more of thesphere's volume may lie outside the brain volume. If subsequent modelingplaces dipoles in this non-overlapping region, this is a large number ofdipoles that physically do not exist.

In FIG. 3B, the sphere 340B has a center 342B that is outwards of thelocal surface patch 314B. That is, the center 342B of the sphere and theMEG sensor 310B are both located on the outward side of the localsurface patch 314B. This may occur, for example, if the sample pointsfor the surface patch 314B suggest that it is locally concave. In thisexample, the sphere 340B typically is not overlapping with the brainvolume. As in FIG. 3A, this may also be problematic because dipoleslocated in the sphere 340B will lie outside the brain volume.

FIG. 4 is a flow diagram for correcting a multi-sphere head model.Spheres in the OSM that are ghost spheres are identified 410. This maybe accomplished using the characteristics of ghost spheres describedabove. If a sphere's center lies outside the brain volume or if asignificant fraction of a sphere falls outside the brain volume, it maybe identified as a ghost sphere. The ghost spheres are not suitable formodeling dipole localization in the brain volume, typically because asignificant fraction of the ghost sphere falls outside the brain volume.As a result, the ghost spheres are replaced 412 by other spheres thatare not ghost spheres, resulting in a corrected OSM.

Various approaches to generate replacement spheres are described below.In one correction approach, ghost spheres are replaced by the globalsphere generated for the single sphere model. This results in a hybridapproach. Some of the MEG sensors will use the local sphere generatedfor that sensor, and the rest of the MEG sensors will use the globalsphere. In a variation, the global sphere may be generated based on onlythose MEG sensors that have ghost spheres, rather than based on all MEGsensors as is the case in a true SSM approach.

In another approach, the replacement sphere is selected from a family ofcandidate replacement spheres. For example, the family of candidatereplacement spheres may all have centers that lie along a common line:the line defined by the MEG sensor and the point on the brain surfaceclosest to the MEG sensor, or the line defined by the MEG sensor and thecenter of the global sphere described previously, or the line defined bythe MEG sensor and the center of the brain volume. The family ofcandidate replacement spheres may also be constrained in diameter. Forexample, they may all have diameters that do not exceed a smallestdiameter that completely encloses the brain volume. As another example,the family of candidate replacement spheres may all pass through thepoint on the brain surface closest to the MEG sensor. In one approachthe replacement sphere is selected from the family of candidatereplacement spheres based on a fit between the replacement sphere andthe brain surface.

FIGS. 5-9 show some examples. FIG. 5 shows a family of candidatereplacement spheres 540 defined as follows. A line 548 is defined by theMEG sensor 510 and the point 514 on the brain surface that is closest tothe MEG sensor. The centers of the replacement spheres 540 lie on line548 on the inward side of point 514. In addition, the replacementspheres 540 are contrained to include this surface point 514. Increasingthe diameter of the sphere yields the family of candidate replacementspheres 540. In this example, the maximum diameter is also constrainedby the smallest sphere that encloses the brain volume.

One of the candidate spheres is selected as the replacement sphere,typically based on a fit between the replacement sphere and the brainsurface. The selection can be solved as an optimization problem. Thefamily of candidate spheres can be parameterized as a function of thesphere diameter in a range of [0, max diameter]. The problem is then toselect the sphere diameter that optimizes a cost function. Examples ofcost functions are based on local curvature fitting based on the L1error, the L2 error, or using eigen-solvers (both analytical andapproximation classes of sphere fitting fitting the curvature of a localsurface patch).

In FIG. 5, the centers of the candidate replacement spheres wereconstrained to lie along line 548. Other lines could be selected, asshown in FIG. 6A. FIG. 6A shows the following points: location 610 ofthe MEG sensor, the closest surface point 614 to the MEG sensor, thecenter 632 of the global sphere (from the SSM of FIG. 2A), and thecenter 622 of the brain volume. Different pairs of points define otherlines: line 646 through the MEG sensor 610 and the SSM center 632, line647 through the MEG sensor 610 and the brain center 622, line 648through surface point 614 and the SSM center 632, and line 649 throughsurface point 614 and the brain center 622, for example. The linesthrough surface point 614 are dashed in order to more easily distinguishthe lines from each other. Other families of candidate replacementspheres may be defined by requiring the center of the replacement sphereto lie on any of these lines. Other lines may also be used, for examplelines that are normal to the surface of the brain.

The locus of possible locations for the sphere's center may also be anarea or volume, rather than a line. For example, as shown in FIG. 6B, itmay be the triangle with vertices 610-632-622, but considering onlythose points that are on the inward side of point 614. The resultinglocus of possible center points is the trapezoid 646. FIG. 7 showsanother example where the location of the MEG sensor is defined by anarea 710 rather than a point, and the closest surface patch is alsodefined by an area 714 rather than a point. The locus of possible centerpoints is defined by a projection of area 710 through area 714, whichdefines a three-dimensional volume 746. FIG. 7A shows a more restrictiveprojection 746A and FIG. 7B shows a more expansive projection 746B.Volumes may also be defined by starting with a line or area and defininga volume that is within a certain distance of the line or area.

The region of interest, whether it is a line, area or volume, istypically defined by at least two of the following: (a) the location ofthe MEG sensor (whether defined as a point, area or volume), (b) theregion of brain surface closest to the MEG sensor (which is typically apoint or surface area), and (c) the location of the brain volume (e.g.,the center of the SSM global sphere, or the centroid or center of massof the brain volume).

The family of candidate replacement spheres may also be constrained tobe smaller than a maximum size. The maximum diameter of the replacementsphere may be selected so that the replacement sphere is not a ghostsphere. FIG. 8 shows the same situation as FIG. 5 but also shows spheresof different maximum diameters, assuming that the center of the spherelies along line 848 and the sphere includes surface point 814. Forsphere 840A, the maximum diameter is defined by the largest sphere thatis enclosed by the brain volume. For sphere 840B, it is defined by thesmallest sphere that encloses the brain volume (same as in FIG. 5). Forsphere 840C, it is defined by requiring that the center 842C of thesphere remains inside the brain volume.

In FIG. 5, the family of candidate replacement spheres is alsoconstrained to include point 514, which is the point closest to the MEGsensor. That is, every candidate replacement sphere 540 passes throughpoint 514. Other variations of this constraint are also possible. InFIG. 9, the candidate replacement spheres 940 are constrained to havecenters that lie on line 948, defined by the location 910 of the MEGsensor and the closest surface point 914. However, the spheres are notrequired to all pass through the surface point 914. Rather, each sphere940 is located so that it makes a best fit to a local patch of thebrain's surface. Thus, spheres 940 may be shifted slightly off of point914.

In some implementations, a user interface allows the user to control thecorrection process. In FIG. 10, the user interface shows a ghost sphere1040 that lies outside the brain 1020. The user is prompted 1070 whethercorrection should be attempted. The user responds by giving a userinstruction whether to compute a replacement sphere for that particularghost sphere. The next screen of the user interface could then show thecomputed replacement sphere and prompt the user whether to replace theghost sphere with the calculated replacement sphere. The user interfacedisplays the various spheres in relation to the brain so that the usercan visualize the situation.

In yet another approach, rather than correcting ghost spheres, amulti-sphere head model is generated subject to constraints that preventthe generation of ghost spheres in the first place. For example, thecenters of the spheres may be constrained to lie inside the brainvolume. The diameters of the spheres may be constrained so that they donot exceed some maximum, for example the diameter of the smallest spherethat completely encloses the brain volume. The constraints describedabove for defining families of candidate replacement spheres may also beused as constraints to prevent the generation of ghost spheres in thefirst place.

As a final example, ghost spheres may result from fitting too few datapoints. To avoid this, the spheres may be fit to a set of points on thebrain surface, but subject to the constraint that at least a predefinednumber of points are used to fit the sphere.

Although the detailed description contains many specifics, these shouldnot be construed as limiting the scope of the invention but merely asillustrating different examples. It should be appreciated that the scopeof the disclosure includes other embodiments not discussed in detailabove. For example, ellipsoids or other shapes may be used instead ofspheres. In that case, a multi-ellipsoid head model is developed inplace of a multi-sphere head model and the concept of ghost spheres isreplaced by ghost ellipsoids. Various other modifications, changes andvariations which will be apparent to those skilled in the art may bemade in the arrangement, operation and details of the method andapparatus disclosed herein without departing from the spirit and scopeas defined in the appended claims. Therefore, the scope of the inventionshould be determined by the appended claims and their legal equivalents.

Alternate embodiments are implemented in computer hardware, firmware,software, and/or combinations thereof. Implementations can beimplemented in a computer program product tangibly embodied in acomputer-readable storage device for execution by a programmableprocessor; and method steps can be performed by a programmable processorexecuting a program of instructions to perform functions by operating oninput data and generating output. Embodiments can be implementedadvantageously in one or more computer programs that are executable on aprogrammable computer system including at least one programmableprocessor coupled to receive data and instructions from, and to transmitdata and instructions to, a data storage system, at least one inputdevice, and at least one output device. Each computer program can beimplemented in a high-level procedural or object-oriented programminglanguage, or in assembly or machine language if desired; and in anycase, the language can be a compiled or interpreted language. Suitableprocessors include, by way of example, both general and special purposemicroprocessors. Generally, a processor will receive instructions anddata from a read-only memory and/or a random-access memory. Generally, acomputer will include one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as EPROM, EEPROM, and flashmemory devices; magnetic disks such as internal hard disks and removabledisks; magneto-optical disks; and CD-ROM disks. Any of the foregoing canbe supplemented by, or incorporated in, ASICs (application-specificintegrated circuits), FPGAs and other forms of hardware.

What is claimed is:
 1. A method implemented on a computer system, thecomputer system executing instructions to execute the method forgenerating a multi-ellipsoid head model used in dipole localization fora set of magnetic field sensors (MEG sensors), the method comprising:accessing locations of each MEG sensor from the set of MEG sensors; andfor each MEG sensor from the set of MEG sensors, computing acorresponding ellipsoid subject to a plurality of constraints thatprevent generation of a ghost ellipsoid, the computed ellipsoids used tomodel dipole localization in a brain's volume; wherein the plurality ofconstraints comprise: a first constraint that prevents generation ofcomputed ellipsoids that completely encloses the brain's volume but havea center outside the brain's volume; a second constraint that preventsgeneration of computed ellipsoids that lie entirely outside the brain'svolume; and a third constraint that requires that the center of thecomputed ellipsoid lies inside the brain's volume.
 2. Thecomputer-implemented method of claim 1 wherein the plurality ofconstraints further comprise a fourth constraint that preventsgeneration of computed ellipsoids that have a volume that is at leastfifty percent non-overlapping with the brain's volume.
 3. Thecomputer-implemented method of claim 1 wherein at least one of thecomputed ellipsoids is a global sphere that is fit to an entire surfaceof the brain.
 4. The computer-implemented method of claim 1 wherein theplurality of constraints further comprise a fourth constraint that amajor axes of computed ellipsoids do not exceed a diameter of a smallestsphere that completely encloses the brain's volume.
 5. Thecomputer-implemented method of claim 1 wherein computing thecorresponding ellipsoid comprises fitting an ellipsoid to a set ofpoints on the brain surface relevant to the corresponding MEG sensor,and the plurality of constraints further comprise a fourth constraintthat at least a predefined number of points are used to fit theellipsoid.
 6. A method implemented on a computer system, the computersystem executing instructions to execute the method for generating amulti-ellipsoid head model used in dipole localization for a set ofmagnetic field sensors (MEG sensors), the method comprising: accessinglocations of each MEG sensor from the set of MEG sensors; and for eachMEG sensor from the set of MEG sensors, computing a correspondingellipsoid subject to a plurality of constraints that prevent generationof a ghost ellipsoid, the computed ellipsoids used to model dipolelocalization in a brain's volume; wherein the plurality of constraintscomprise: either a first set of constraints comprising (1) a center ofthe computed ellipsoid lies on a line through (a) a location of thecorresponding MEG sensor, and (b) a point on the brain's surface closestto the corresponding MEG sensor; and (2) a major axis of the computedellipsoid is not larger than a diameter of a smallest sphere thatcompletely encloses the brain volume; OR a second set of constraintscomprising (1) the center of the computed ellipsoid lies on a linethrough (a) the location of the corresponding MEG sensor, and (b) acenter of a global sphere that is fit to the entire surface of thebrain; and a third constraint that the computed ellipsoid includes thepoint on the brain's surface closest to the corresponding MEG sensor. 7.The computer-implemented method of claim 6 wherein the plurality ofconstraints include the first set of constraints.
 8. Thecomputer-implemented method of claim 6 wherein the plurality ofconstraints include the second set of constraints.
 9. A methodimplemented on a computer system, the computer system executinginstructions to execute the method for generating a multi-ellipsoid headmodel used in dipole localization for a set of magnetic field sensors(MEG sensors), the method comprising: accessing locations of each MEGsensor from the set of MEG sensors; and for each MEG sensor from the setof MEG sensors, computing a corresponding ellipsoid subject to pluralityof constraints that prevent generation of a ghost ellipsoid, thecomputed ellipsoids used to model dipole localization in a brain'svolume; wherein the plurality of constraints comprise a first constraintthat the computed ellipsoid must have a center that lies along a linethat traverses through at least two of the following three regions: (i)a location of the corresponding MEG sensor, (ii) a region of the brain'ssurface closest to the corresponding MEG sensor, and (iii) a location ofthe brain's volume.
 10. The computer-implemented method of claim 9wherein the line traverses through the location of the corresponding MEGsensor.
 11. The computer-implemented method of claim 9 wherein the linetraverses through the region of the brain's surface closest to thecorresponding MEG sensor.
 12. The computer-implemented method of claim 9wherein the line is normal to the brain's surface.
 13. Thecomputer-implemented method of claim 9 wherein the plurality ofconstraints further comprise a second constraint that the center of thecomputed ellipsoid must lie within an area or volume defined by at leasttwo of the following three regions: (i) the location of thecorresponding MEG sensor, (ii) the region of the brain's surface closestto the corresponding MEG sensor, and (iii) the location of the brain'svolume.
 14. The computer-implemented method of claim 9 wherein theplurality of constraints further comprise a second constraint that thecomputed ellipsoid must have a major axis that does not exceed a maximumthat is one of: (i) a diameter of a largest sphere in a family ofspheres that meet the first constraint and that is enclosed by thebrain's volume, (ii) a diameter of a smallest sphere in the family thatcompletely encloses the brain's volume, and (iii) a diameter of asmallest sphere in the family that has center inside the brain's volume.15. The computer-implemented method of claim 9 wherein the plurality ofconstraints further comprise a second constraint that the computedellipsoid includes a closest point on the brain surface to thecorresponding MEG sensor.